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of Sciences All rights reserved,HELPING CHILDREN LEARN MATHEMATICS. Mathematics Learning Study Committee,Jeremy Kilpatrick Jane Swafford. and Bradford Findell editors,Center for Education, Division of Behavioral and Social Sciences and Education. National Research Council,National Academy Press,Washington DC. of Sciences All rights reserved, NATIONAL ACADEMY PRESS 2101 Constitution Avenue N W Washington DC 20418.
NOTICE The project that is the subject of this report was approved by the Governing Board of the. National Research Council whose members are drawn from the councils of the National Academy of. Sciences the National Academy of Engineering and the Institute of Medicine The members of the. committee responsible for the report were chosen for their special competences and with regard for. appropriate balance, This study was supported by Contract Grant No ESI 9816818 between the National Academy of. Sciences and the U S Department of Education and the National Science Foundation Any opinions. findings conclusions or recommendations expressed in this publication are those of the author s and. do not necessarily reflect the views of the organizations or agencies that provided support for the project. Library of Congress Cataloging in Publication Data. Adding it up helping children learn mathematics Jeremy Kilpatrick. Jane Swafford and Bradford Findell editors,Includes bibliographical references and index. ISBN 0 309 06995 5 hardcover, 1 Mathematics Study and teaching Elementary United States 2. Mathematics Study and teaching Middle school United States I. Kilpatrick Jeremy II Swafford Jane III Findell Bradford. QA135 5 A32 2001,372 7 dc21,2001001734,Suggesed citation. National Research Council 2001 Adding it up Helping children learn mathematics J Kilpatrick J. Swafford and B Findell Eds Mathematics Learning Study Committee Center for Education. Division of Behavioral and Social Sciences and Education Washington DC National Academy Press. Additional copies of this report are available from National Academy Press 2101 Constitution Avenue. N W Lockbox 285 Washington DC 20055 800 624 6242 or 202 334 3313 in the Washington. metropolitan area Internet http www nap edu,Printed in the United States of America.
Copyright 2001 by the National Academy of Sciences All rights reserved. of Sciences All rights reserved,National Academy of Sciences. National Academy of Engineering,Institute of Medicine. National Research Council, The National Academy of Sciences is a private nonprofit self perpetuating society of. distinguished scholars engaged in scientific and engineering research dedicated to the. furtherance of science and technology and to their use for the general welfare Upon the. authority of the charter granted to it by the Congress in 1863 the Academy has a mandate. that requires it to advise the federal government on scientific and technical matters Dr Bruce. M Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964 under the charter of the. National Academy of Sciences as a parallel organization of outstanding engineers It is. autonomous in its administration and in the selection of its members sharing with the National. Academy of Sciences the responsibility for advising the federal government The National. Academy of Engineering also sponsors engineering programs aimed at meeting national. needs encourages education and research and recognizes the superior achievements of. engineers Dr Wm A Wulf is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to. secure the services of eminent members of appropriate professions in the examination of. policy matters pertaining to the health of the public The Institute acts under the responsi. bility given to the National Academy of Sciences by its congressional charter to be an adviser. to the federal government and upon its own initiative to identify issues of medical care. research and education Dr Kenneth I Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in. 1916 to associate the broad community of science and technology with the Academy s pur. poses of furthering knowledge and advising the federal government Functioning in accor. dance with general policies determined by the Academy the Council has become the prin. cipal operating agency of both the National Academy of Sciences and the National Academy. of Engineering in providing services to the government the public and the scientific and. engineering communities The Council is administered jointly by both Academies and the. Institute of Medicine Dr Bruce M Alberts and Dr Wm A Wulf are chairman and vice. chairman respectively of the National Research Council. of Sciences All rights reserved,of Sciences All rights reserved. MATHEMATICS LEARNING STUDY COMMITTEE,JEREMY KILPATRICK Chair University of Georgia.
DEBORAH LOEWENBERG BALL University of Michigan,HYMAN BASS University of Michigan. JERE BROPHY Michigan State University,FELIX BROWDER Rutgers University. THOMAS P CARPENTER University of Wisconsin Madison. CAROLYN DAY Dayton Public Schools,KAREN FUSON Northwestern University. JAMES HIEBERT University of Delaware,ROGER HOWE Yale University. CAROLYN KIERAN University of Quebec Montreal, RICHARD E MAYER University of California Santa Barbara.
KEVIN MILLER University of Illinois Urbana Champaign. CASILDA PARDO Albuquerque Public Schools,EDGAR ROBINSON Exxon Mobil Corporation Retired. HUNG HSI WU University of California Berkeley,NATIONAL RESEARCH COUNCIL STAFF. JANE SWAFFORD Study Director,BRADFORD FINDELL Program Officer. GAIL PRITCHARD Program Officer,SONJA ATKINSON Administrative Assistant. SPECIAL OVERSIGHT COMMISSION FOR,THE MATHEMATICS LEARNING STUDY.
RONALD L GRAHAM Chair University of California San Diego. DEBORAH LOEWENBERG BALL University of Michigan,IRIS CARL Houston Independent School District. THOMAS P CARPENTER University of Wisconsin Madison. CHRISTOPHER CROSS Council for Basic Education,RONALD DOUGLAS Texas A M University. ROGER HOWE Yale University,LYNNE REDER Carnegie Mellon University. HAROLD STEVENSON University of Michigan,PHILLIP URI TREISMAN University of Texas Austin. of Sciences All rights reserved,of Sciences All rights reserved.
This report has been reviewed in draft form by individuals chosen for. their diverse perspectives and technical expertise in accordance with proce. dures approved by the National Research Council s Report Review Commit. tee The purpose of this independent review is to provide candid and critical. comments that will assist the institution in making its published report as. sound as possible and to ensure that the report meets institutional standards. for objectivity evidence and responsiveness to the study charge The re. view comments and draft manuscript remain confidential to protect the in. tegrity of the deliberative process We wish to thank the following individu. als for their participation in the review of this report. JOHN ANDERSON Carnegie Mellon University,RICHARD A ASKEY University of Wisconsin Madison. ARTHUR BAROODY University of Illinois Urbana Champaign. GUNNAR CARLSSON Stanford University,JERE CONFREY University of Texas. JOHN DOSSEY Illinois State University, JEAN CLAUDE FALMAGNE University of California Irvine. HERBERT GINSBURG Columbia University,KENNETH KOEDINGER Carnegie Mellon University. CAROLYN MAHER Rutgers University, ALFRED MANASTER University of California San Diego.
BETHANY RITTLE JOHNSON Carnegie Mellon University,of Sciences All rights reserved. MARIA SANTOS San Francisco Unified School District. PATRICK THOMPSON Vanderbilt University,ZALMAN USISKIN University of Chicago. Although the reviewers listed above have provided many constructive. comments and suggestions they were not asked to endorse the conclusions. or recommendations nor did they see the final draft of the report before its. release The review of this report was overseen by Ronald L Graham Uni. versity of California San Diego and Patrick Suppes NAS Stanford Univer. sity Appointed by the National Research Council they were responsible for. making certain that an independent examination of this report was carried. out in accordance with institutional procedures and that all review comments. were carefully considered Responsibility for the final content of this report. rests entirely with the authoring committee and the institution. of Sciences All rights reserved,ACKNOWLEDGMENTS, Adding It Up is the product of an 18 month project in which 16 individuals. with diverse backgrounds as a committee reviewed and synthesized relevant. research on mathematics learning from pre kindergarten through grade 8 We. had the good fortune of working with a number of people outside the com. mittee who shared our enthusiasm for this project and we are indebted to. them for the intellectual insights and support that they provided. At a time when mathematics education issues have reached a critical point. both publicly and politically it has become clear that our nation has a respon. sibility to provide guidance and leadership in answering questions about how. to improve mathematics learning for all students We would like to thank our. sponsors the National Science Foundation and the U S Department of Edu. cation for their foresight in providing a timely opportunity to move the debate. forward In particular we thank Janice Earle from the National Science Foun. dation Patricia O Connell Ross from the U S Department of Education. and Judy Wurtzel and Linda Rosen both formerly with the U S Department. of Education for their constant support and interest in this study. During the information gathering phase of our work a number of people. made presentations to the committee on various topics pertaining to math. ematics learning We benefited greatly from their stimulating presentations. and extend our thanks to Jo Boaler Stanford University School of Education. Douglas Carnine University of Oregon National Center to Improve the Tools. of Educators Paul Clopton Mathematically Correct Megan Franke Univer. sity of California Los Angeles Graduate School of Education and Information. Studies and Judith Sowder San Diego State University Center for Research. in Mathematics and Science Education Additionally we would like to thank. of Sciences All rights reserved,x ACKNOWLEDGMENTS, Steven Stahl and Donna Alvermann University of Georgia and Susan Burns. George Mason University for providing us with insights about the parallels. between mathematics and reading And we are grateful to Carne Barnett. WestEd Regional Education Laboratory Deborah Schifter Education. Development Center Patricia Campbell University of Maryland Center for. Mathematics Education Anne Morris University of Delaware School of. Education and Mary Kay Stein University of Pittsburgh Learning Research. and Development Center for providing information about specific programs. in elementary mathematics or teacher development, We also wish to acknowledge the people who provided informative com.
missioned papers that expanded and enhanced our collective thinking In. particular we appreciate the work of Rolf Blank Council of Chief State School. Officers Graham Jones Cynthia Langrall and Carol Thornton Illinois State. University Gloria Ladson Billings and Richard Lehrer University of. Wisconsin Madison and Denise Mewborn University of Georgia We also. thank Douglas McLeod and Judith Sowder San Diego State University and. Les Steffe University of Georgia for their assistance with research reviews. for specific topics on which we had questions, While writing the final draft of this report we commissioned several chap. ter reviews that strengthened our research synthesis and focused our prose. Many thanks to Kathleen Cramer University of Minnesota James Kaput. University of Massachusetts Dartmouth Mary Lindquist Columbus State. University Thomas Post University of Minnesota and Edward Rathmell. University of Northern Iowa, While the individuals listed above have provided many constructive com. ments and suggestions responsibility for the final content of this report rests. solely with the authoring committee and the National Research Council. Finally we would like extend our sincere thanks to several individuals. within the National Research Council and in other places who made signifi. cant contributions to our work Rodger Bybee former Executive Director for. the Center and Patrice Legro former Division Director for Special Projects. for providing the initial impetus for this project and getting it off to a strong. start Gail Pritchard Program Officer for keeping us on the straight and narrow. in complying with the myriad of NRC policies and procedures Bradford. Findell Program Officer for researching drafting and editing many sections. of the report Michael J Feuer Executive Director for the Center for Educa. tion CFE for providing key advice Kirsten Sampson Snyder Reports Officer. for CFE for guiding us through the report review process Steve Olson and. Yvonne Wise for providing editorial assistance Sally Stanfield National. Visit the National Academies Press online the authoritative source for all books from the National Academy of Sciences the National Academy of Engineering the Institute of Medicine and the National Research Council Download hundreds of free books in PDF Read thousands of books online for free

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